STATEMENT OF PROBLEM

Consider a hemispherical loaf of crusty French bread of radius 8". Alice and Bill just love the crust of the bread and are having 6 friends over for dinner. They wish to slice the bread so that each of the 8 dinner party members will get an equal amount of crust.

Alice suggests that they just cut the bread vertically (parallel to a plane going through the center) into pieces each one-eighth of the diameter wide. She claims that in this way each person will have the same amount of crust.

Bill says, "Just because the width of each piece is the same does not mean the amount of crust on each piece is the same."

Formulate this problem mathematically and settle the argument.